It is known in the air valve art to provide four-way valves which employ a sliding type of valve spool with annular seal means. It is also known to operate such sliding valve spools by direct solenoid operation. A disadvantage of the last mentioned prior art four-way valves is that in order to provide a high flow of fluid, as air, a long stroke of the valve spool is required, together with a large solenoid for operating the same, and a large valve structure for housing the valve spool and the solenoid. It is also known in the air valve art to provide three-way poppet type valves for controlling the flow of fluid, such as air in a fluid flow control system. An advantage of a poppet type valve is that maximum flow can be provided with a short stroke. Heretofore, a problem in producing a four-way poppet valve was the provision of a poppet valve structure which was capable of efficiently and simultaneously sealing a pair of poppet seals when the valve spool carrying the poppet valves was operated directly by a solenoid. Examples of prior art three-way poppet valves are shown in U.S. Pat. Nos. 4,271,868, 4,298,027 and 4,407,323.